Rational man dealing with Irrational numbers.
The Greeks thought that all numbers could be written as fractions because if you think about it, you can pick any two fractions, no matter how close to each other on the real number line, add them together and divide by 2 to find a fraction between them.
But the Lord had a treat for all human wisdom and knowledge and put two of the most common shapes used (a square, and a circle) with parts who's lengths could not be written as fractions. The length of the diagonal of any square with rational (fractions with integer numerators/denominators [with the exception of zero as denominator]), each side = X, cannot be written as a fraction as and the diagonal has length, diagonal = X times the square root of 2 (and the square root of 2 cannot be written as a fraction.
For the circle, if you simply take the circumference of a circle divided by its diameter you get pi and again pi cannot be written as a fraction.
In the next story tab I'll show how the story continues as not only did the Greeks call the non perfect roots irrational but irrational numbers contain two types (namely algebraic irrational [like the square root of 2] and transcendental irrational numbers [like pi] and I'll show how there has to be more transcendental irrational numbers than rational number even though the set of rational numbers is infinite.
On top of that, I'll show that even though the transcendental irrational numbers is a larger infinity than the rational number infinity; mankind can place all the transcendental numbers currently know in a very short and transcendental numbers are the most complicated set of numbers of all the number systems. Anyone who can find and prove they've found a new transcendental number can earn their doctorate in Math (it is that hard to add one to the list)!
Some places to find lists of transcendental numbers are: The Top 15 Transcendental Numbers, and What are Transcendental Numbers. The latter site will back up my claim that the Transcendental Numbers are a non-countable set where the rational numbers (fractions) are a countable set AND that it is really difficult to prove a number is transcendental or not.
For the circle, if you simply take the circumference of a circle divided by its diameter you get pi and again pi cannot be written as a fraction.
In the next story tab I'll show how the story continues as not only did the Greeks call the non perfect roots irrational but irrational numbers contain two types (namely algebraic irrational [like the square root of 2] and transcendental irrational numbers [like pi] and I'll show how there has to be more transcendental irrational numbers than rational number even though the set of rational numbers is infinite.
On top of that, I'll show that even though the transcendental irrational numbers is a larger infinity than the rational number infinity; mankind can place all the transcendental numbers currently know in a very short and transcendental numbers are the most complicated set of numbers of all the number systems. Anyone who can find and prove they've found a new transcendental number can earn their doctorate in Math (it is that hard to add one to the list)!
Some places to find lists of transcendental numbers are: The Top 15 Transcendental Numbers, and What are Transcendental Numbers. The latter site will back up my claim that the Transcendental Numbers are a non-countable set where the rational numbers (fractions) are a countable set AND that it is really difficult to prove a number is transcendental or not.